Cambridge Core – Computing: General Interest – Computability and Logic – by George S. Boolos. but instructors who adopt Computability & Logic as a textbook are hereby authorized to copy and distribute the present Part A. This permission does not extend. Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the.

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You should probably pick up a book on how to effectively, and elegantly, write a proof before reading this.

This is all well and good, but I was expecting much more detail and motivation, given the impressive motivation found elsewhere in the book. Jun 22, Warunika Ranaweera rated it it was amazing.

Dec 06, Chris Rhodes rated it really liked it Shelves: A vast improvement over the fourth edition. Comptuability book excels at showing you the actual mechanisms behind results that are often mentioned but seldom exposed.

Diagonalization stops the buck. It’s good clean fun to see these things play out in front of you, instead of just hearing the results secondhand. This result was surprising, and the proof is a fun one.

G. S. Boolos & R. C. Jeffrey, Computability and Logic – PhilPapers

This may all seem a bit abstract, especially following all the computationally-motivated content above. Want to Read saving…. Sets and relations are called “primitive recursive” if their indicator functions can loyic constructed from primitive recursive building blocks. This book comes highly recommended, especially to people just getting interested in the fields of computability and logic. The result is shown in this chapter by elimination ane quantifiers: It’s not a very in-depth introduction.


Marcin Tkaczyk – – Roczniki Filozoficzne: When you realize how much can be enumerated there’s a one-to-one mapping between natural numbers and all finite subsets of the natural numbers!

Alternatively, you can resolve to deal only with sentences where all the quantifiers come first. Andrada Pop rated it it was amazing Mar 31, First order logic becomes undecidable when you add the first two-place relation symbol. Return to Book Page. This chapter develops an arithmetization of computabiljty syntax first-order logic, and of the proof system sketched in the previous chapter.

That concludes the summary. Generally speaking, we can define sets and relations by indicator functions which distinguish between elements that are in a set from elements that are not. Adam Gardner rated it really liked it Dec 21, Compactness computwbility explained, but not proven. Setup an account with your affiliations in order to access resources via your University’s proxy server Configure custom proxy use this if your affiliation does not provide a proxy.

The second chapter of Computability and Logic is a clever and easy introduction to diagonalization, and I highly recommend it to newcomers. Don’t pick it up for that reason, no matter what Luke tells you: This transition is motivated computationally: This chapter is entirely devoted to a proof of the compactness theorem.

Book Review: Computability and Logic

Chapters also come highly recommended if you want to really understand incompleteness and undecidability. Johannes Korbmacher – – Journal of Philosophical Logic 47 2: I’m reviewing the books on the MIRI course list. The FOL chapters could loogic done with some rework. Lattice Representations for Computability Theory.


That said, it’s not a good introduction to modal provability logic. Fejer – – Annals of Pure and Applied Logic 94 Its contents are summarized below. Computability and Logic is a wonderful book. If there’s a one-to-one mapping between two compjtability, those sets are “the same size”.

Computability and Logic by George S. Boolos

I can’t do it justice in a few mere paragraphs: It also introduces the concepts of soundness and completeness. Chapter 18 in particular is quite relevant to some of MIRI’s recent work, and is good to know in the LessWrong circles. Ocmputability a great way to brush up on your understanding of incompleteness, if you think you have to.

If you’re new to the ideas of arithmetization and representability, then you don’t want to read the next three chapters without reading this. bklos

Read it if you’re curious, skip it if you’re not. For those of you who don’t know, the Turing Machine is an idealized computation engine which can compute answers to a very large class of problems.

It also sets up Model Theory nicely and has a brief intro to modal logic. This chapter introduces second order logic, and shows some basic results it’s not compact, etc.

However, this book doesn’t just tell you that result, it shows it to you.